A138106 - OEIS

A138106

A triangular sequence of coefficients based on the expansion of a Morse potential type function: p(x,t) = exp(x*t)*(exp(-2*t) - 2*exp(-t)).

-1, 0, -1, 2, 0, -1, -6, 6, 0, -1, 14, -24, 12, 0, -1, -30, 70, -60, 20, 0, -1, 62, -180, 210, -120, 30, 0, -1, -126, 434, -630, 490, -210, 42, 0, -1, 254, -1008, 1736, -1680, 980, -336, 56, 0, -1, -510, 2286, -4536, 5208, -3780, 1764, -504, 72, 0, -1, 1022, -5100, 11430, -15120, 13020, -7560, 2940, -720, 90, 0, -1

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,4

COMMENTS

Row sums are: {-1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1,...}.

The Morse potential is identified with simple intermolecular energy to distance relationships.

REFERENCES

A. Messiah, Quantum mechanics, vol. 2, p. 795, fig.XVIII.2, North Holland, 1969.

LINKS

G. C. Greubel, Rows n = 1..100 of triangle, flattened

FORMULA

p(x,t) = exp(x*t)*(exp(-2*t) - 2*exp(-t)) = Sum_{n>=0} P(x,n)*t^n/n!.

EXAMPLE

Triangle begins as:

-1;

0, -1;

2, 0, -1;

-6, 6, 0, -1;

14, -24, 12, 0, -1;

-30, 70, -60, 20, 0, -1;

62, -180, 210, -120, 30, 0, -1;

-126, 434, -630, 490, -210, 42, 0, -1;

254, -1008, 1736, -1680, 980, -336, 56, 0, -1;

-510, 2286, -4536, 5208, -3780, 1764, -504, 72, 0, -1;

1022, -5100, 11430, -15120, 13020, -7560, 2940, -720, 90, 0, -1;

.....

MATHEMATICA

p[t_] = Exp[x*t]*(Exp[ -2*t] - 2*Exp[ -t]);

Table[ ExpandAll[n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 0, 10}];

Table[n!* CoefficientList[SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}]//Flatten

CROSSREFS

Sequence in context: A264550 A089949 A085845 * A131689 A278075 A114329

Adjacent sequences: A138103 A138104 A138105 * A138107 A138108 A138109

KEYWORD

tabl,sign

AUTHOR

Roger L. Bagula, May 03 2008

EXTENSIONS

Edited by G. C. Greubel, Apr 01 2019

STATUS

approved